10:[["$","title","0",{"children":"CUET Mathematics - The function, f(x) = x - 1/x is | PYQs + Solutions | AfterBoards"}],["$","meta","1",{"name":"description","content":"undefined To determine whether f(x) = x - 1/x is increasing or decreasing, find the derivative and check its sign.

f(x) = x - 1/x Rewrite as: f(x) = x - x^-1 Differentiate: f'(x) = 1 - (-1)x^-2 f'(x) = 1 + 1/x^2

For f'(x) = 1 + 1/x^2: Since x^2 is always positive for x 0, then 1/x^2 is always positive. Therefore: f'(x) = 1 + 1/x^2 > 1 > 0 Since f'(x) > 0 for all x 0, the function is increasing.

The function f(x) = x - 1/x is not defined at x = 0 (division by zero). The domain is x (-\\∞, 0) (0, \\∞).

Therefore, the function is increasing for all x (-\\∞, 0) (0, \\∞)."}],["$","link","2",{"rel":"manifest","href":"https://www.afterboards.in/manifest.json","crossOrigin":"$undefined"}],["$","meta","3",{"name":"keywords","content":"CUETMAT,MAT,Calculus,Application of Derivatives"}],["$","meta","4",{"name":"robots","content":"index, follow"}],["$","meta","5",{"name":"category","content":"education"}],["$","meta","6",{"name":"google-site-verification","content":"google"}],["$","meta","7",{"property":"og:title","content":"CUET Mathematics - The function, f(x) = x - 1/x is | PYQs + Solutions"}],["$","meta","8",{"property":"og:description","content":"undefined To determine whether f(x) = x - 1/x is increasing or decreasing, find the derivative and check its sign.

f(x) = x - 1/x Rewrite as: f(x) = x - x^-1 Differentiate: f'(x) = 1 - (-1)x^-2 f'(x) = 1 + 1/x^2

For f'(x) = 1 + 1/x^2: Since x^2 is always positive for x 0, then 1/x^2 is always positive. Therefore: f'(x) = 1 + 1/x^2 > 1 > 0 Since f'(x) > 0 for all x 0, the function is increasing.

The function f(x) = x - 1/x is not defined at x = 0 (division by zero). The domain is x (-\\∞, 0) (0, \\∞).

Therefore, the function is increasing for all x (-\\∞, 0) (0, \\∞)."}],["$","meta","9",{"property":"og:url","content":"https://www.afterboards.in/past-year-questions/cuet-mathematics/2025/slot-17/3"}],["$","meta","10",{"property":"og:site_name","content":"AfterBoards | CUET Mathematics Preparation"}],["$","meta","11",{"property":"og:image","content":"https://www.afterboards.in/pyp/AfterBoards%20CUET%20Past%20Year%20Papers%20with%20Solutions.webp"}],["$","meta","12",{"property":"og:type","content":"website"}],["$","meta","13",{"name":"twitter:card","content":"summary_large_image"}],["$","meta","14",{"name":"twitter:site","content":"afterboards.in"}],["$","meta","15",{"name":"twitter:title","content":"CUET Mathematics - The function, f(x) = x - 1/x is | PYQs + Solutions"}],["$","meta","16",{"name":"twitter:description","content":"undefined To determine whether f(x) = x - 1/x is increasing or decreasing, find the derivative and check its sign.

f(x) = x - 1/x Rewrite as: f(x) = x - x^-1 Differentiate: f'(x) = 1 - (-1)x^-2 f'(x) = 1 + 1/x^2

For f'(x) = 1 + 1/x^2: Since x^2 is always positive for x 0, then 1/x^2 is always positive. Therefore: f'(x) = 1 + 1/x^2 > 1 > 0 Since f'(x) > 0 for all x 0, the function is increasing.

The function f(x) = x - 1/x is not defined at x = 0 (division by zero). The domain is x (-\\∞, 0) (0, \\∞).

Therefore, the function is increasing for all x (-\\∞, 0) (0, \\∞)."}],["$","meta","17",{"name":"twitter:image","content":"https://www.afterboards.in/pyp/AfterBoards%20CUET%20Past%20Year%20Papers%20with%20Solutions.webp"}],["$","link","18",{"rel":"shortcut icon","href":"https://www.afterboards.in/favicon.ico","type":"image/x-icon","sizes":"48x48"}],["$","link","19",{"rel":"icon","href":"https://www.afterboards.in/favicon.ico","type":"image/x-icon","sizes":"48x48"}],"$L17","$L18","$L19","$L1a","$L1b","$L1c","$L1d"]

CUET Mathematics 2025 30 May Shift 2 PYQs

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