Let f- be defined asfx - 10x - 7- Find the function g- such that gof-fog-I-

Solve to calculate g:R→ R. Given: nbsp;f:ℝ→ℝ be defined as f(x) = 10x + 7 Let g is the inverse of f Again, let f(x) = y y = 10x + 7 y 7 = 10x 10x = y 7 x= ...

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Standard XII

Mathematics

Complex Numbers

Let f:ℝ→ℝ be ...

Question

Let $f : R \to R$ be defined as
f(x) = 10x + 7. Find the function $g : R \to R$ such that $g o f = f o g = I_{R}$

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Solution

Solve to calculate $g : R \to R$ .
Given: $f : R \to R$ be defined as f(x) = 10x + 7
Let $g$ is the inverse of $f$
Again, let $f (x) = y$
$y = 10 x + 7$
$y - 7 = 10 x$
1 $0 x = y - 7$
$x = \frac{y - 7}{10}$
Let $g (y) =$ $\frac{y - 7}{10}$
where $g : R \to R$
$g o f = g (f (x)) = g (10 x + 7)$
= $\frac{(10 x + 7) - 7}{10}$
= $\frac{10 x + 7 - 7}{10}$
= $\frac{10 x}{10} = x$
$g o f = I_{R}$
$f o g = f (g (y))$
$= f (\frac{y - 7}{10})$
$= 10 (\frac{y - 7}{10}) + 7 = y - 7 + 7$

$= y + 0 = y$

$= I_{R}$

Since, $g o f = f o g = I_{R}$

So, $g (x) = \frac{x - 7}{10} .$

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Let $f : R \to$ be defined as f(x) =10x +7. Find the function $g : R \to R$ such that gof =fog = $I_{R}$ .

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Complex Numbers

Standard XII Mathematics

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Let f:R→R be defined as f(x) = 10x + 7. Find the function g:R→R such that gof=fog=IR

Let $f : R \to R$ be defined as
f(x) = 10x + 7. Find the function $g : R \to R$ such that $g o f = f o g = I_{R}$