Question

Need explanation 20 points The function f is such that f(x) = 2x - 6 Find f^-1(x)

Answer 1

HEYA! <3

Explanation :

GIVEN :

• f(x) = 2x - 6

TO FIND :

• Inverse of f(x) i.e $f ^{ - 1} (x)$

SOLUTION :

FOLLOW THESE THREE STEPS :

• LET Y = f(x)

$\longrightarrow \tt{y = 2x - 6}$

$\longrightarrow{ \tt{ \: 2x - 6 = y}}$

• MAKE X A SINGLE TERM IN LHS SIDE

$\longrightarrow{ \tt{2x = y + 6}}$

$\longrightarrow{ \tt{x = \frac{y + 6}{2} }}$

• INTERCHANGE THE VALUE OF X AND Y

$\longrightarrow{ \tt{y = \frac{x + 6}{2} }}$

Hence ,

$\boxed{ \boxed{ {f}^{ - 1} (x) = \sf{ \bold{ \frac{x + 6}{2} }}}}$

Hope I helped!

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