f-3x-1-g-1-5x-2-2-g-o-f-4-

Question Number 151758 by mathdanisur last updated on 22/Aug/21

f (3 x + 1) = g^{- 1} ({5 x}^{2} - 2)

{(g o f)}^{^{'}} (4) = ?

Commented by otchereabdullai@gmail.com last updated on 23/Aug/21

nice!

Answered by Olaf_Thorendsen last updated on 22/Aug/21

f (3 x + 1) = g^{- 1} (5 x^{2} - 2)

g o f (3 x + 1) = g o g^{- 1} (5 x^{2} - 2) = 5 x^{2} - 2

3 {(g o f)}^{'} (3 x + 1) = 10 x

{(g o f)}^{'} (3 x + 1) = \frac{10}{3} x

{(g o f)}^{'} (3 \times 1 + 1) = {(g o f)}^{'} (4) = \frac{10}{3} \times 1 = \frac{10}{3}

Commented by mathdanisur last updated on 23/Aug/21

Thank you Ser

Answered by mindispower last updated on 22/Aug/21

g o f (3 x + 1) = 5 x^{2} - 2

\frac{d}{d x} g o f (3 x + 1) = 10 x \Rightarrow 3 g^{'} o f (3 x + 1) = 10 x

x = 1 \Rightarrow {(g o f)}^{'} (4) = \frac{10}{3}

Commented by mathdanisur last updated on 23/Aug/21

Thank you Ser