Let f : R → R : f(x) = 10x + 7. Find the function g : R→ R : g o f

1.	Let f : R → R : f(x) = 10x + 7. Find the function g : R→ R : g o f = f o g = Ig.
Answer» To find: the function g : R → R : g o f = f o g = I_g Formula used: (i) g o f = g(f(x)) (ii) f o g = f(g(x)) Given: f : R → R : f(x) = 10x + 7 We have, f(x) = 10x + 7 Let f(x) = y ⇒ y = 10x + 7 ⇒ y – 7 = 10x \(\Rightarrow x= \frac{y-7}{10}\) Let \(g(y)=\frac{y-7}{10}\) where g: R → R g o f = g(f(x)) = g(10x + 7)\(=\frac{(10x+7)-7}{10}\) = x = I_^g f o g = f(g(x)) =\(f(\frac{x-7}{10})\) \(=10(\frac{x-7}{10})\) \(=10(\frac{x-7}{10})+7\) = x – 7 + 7 = x Clearly g o f = f o g = I_g _{\(g(x)=\frac{x-7}{10}\)}

Let f : R → R : f(x) = 10x + 7. Find the function g : R→ R : g o f = f o g = Ig.

Answer»

To find: the function g : R → R : g o f = f o g = I_g

Formula used: (i) g o f = g(f(x))

(ii) f o g = f(g(x))

Given: f : R → R : f(x) = 10x + 7

We have,

f(x) = 10x + 7

Let f(x) = y

⇒ y = 10x + 7

⇒ y – 7 = 10x

\(\Rightarrow x= \frac{y-7}{10}\)

Let \(g(y)=\frac{y-7}{10}\) where g: R → R

g o f = g(f(x)) = g(10x + 7)\(=\frac{(10x+7)-7}{10}\)

= x

= I_^g

f o g = f(g(x)) =\(f(\frac{x-7}{10})\)

\(=10(\frac{x-7}{10})\)

\(=10(\frac{x-7}{10})+7\)

= x – 7 + 7

= x

Clearly g o f = f o g = I_g

_{\(g(x)=\frac{x-7}{10}\)}