JEE Mains · Maths · STD 12 - 6. Application of derivatives
Let \(f\) and \(g\) be two differentiable functions on \(R\) such that \(f'(x) > 0\) and \(g'(x) < 0\) for all \(x\in R\) .Then for all \(x\)
- A \(f(g (x)) > f(g(x- 1))\)
- B \(f(g (x)) > f(g(x + 1))\)
- C \(g(f(x)) >g(f( x- 1))\)
- D \(g(f(x)) < g(f( x + 1))\)
Answer & Solution
Correct Answer
(B) \(f(g (x)) > f(g(x + 1))\)
Step-by-step Solution
Detailed explanation
since \(f^{\prime}(x)>0\) and \(g^{\prime}(x)<0,\) therefore \(f(x)\) is increasing function and \(g(x)\) is decreasing function. \(\Rightarrow f(x+1)>f(x)\) and \(g\left( {x + 1} \right) < g\left( x \right)\)…
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