Let f : R -> R be defined as f(x) = x³ + x – 5

If g(x) is a function such that f(g(x)) = x, $\forall$ ‘x’ $\in$ R, then g’ (63) is equal to……….

Option 1 -

$\frac{1}{49}$

Option 2 -

$\frac{3}{49}$

Option 3 -

$\frac{43}{49}$

Option 4 -

$\frac{91}{49}$

2 Views | Posted 3 months ago

Asked by Shiksha User

1 Answer

Answered by

Vishal Baghel | Contributor-Level 10

3 months ago

Correct Option - 1

Detailed Solution:

$f (g (x)) = x \forall x \in R$

$\Rightarrow g (x) = f^{- 1} (x)$

For y = g (x)

x = y³ + y – 5

$\frac{d x}{d y} = 3 y^{2} + 1 \Rightarrow g' (63) = \frac{1}{3 (16) + 1} = \frac{1}{49}$

$g' (63) = (\frac{d y}{d x})$

$(\begin{array}{l} x = 63 \\ y = 4 \end{array})$

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Let f : R -> R be defined as f(x) = x³ + x – 5

If g(x) is a function such that f(g(x)) = x, $\forall$ ‘x’ $\in$ R, then g’ (63) is equal to……….

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Let f : R -> R be defined as f(x) = x3 + x – 5 If g(x) is a function such that f(g(x)) = x, ∀ ‘x’ ∈ R, then g’ (63) is equal to……….

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Let f : R -> R be defined as f(x) = x³ + x – 5

If g(x) is a function such that f(g(x)) = x, $\forall$ ‘x’ $\in$ R, then g’ (63) is equal to……….