Question

Find f(g(x)) and g (f(x)) and determine whether each pair of functions ƒ and g are inverses of each other. f(x)=3x+8 and g(x) = (x-8)/3

Accepted Answer

First, find the composition $$ f(g(x))  by $$substituting $$ g(x) $$ into $$ f(x) . $$This means replacing every $$ x  in$$ $$ f(x) = 3x + 8 $$ with $$ g(x) = \frac{x - 8}{3} . So$$, write $$ f(g(x)) = 3 \left( \frac{x - 8}{3} \right) + 8 . $$Next, simplify the expression for $$ f(g(x))  by $$performing the multiplication and addition inside the function. Multiply 3 by $$ \frac{x - 8}{3} $$ and then add 8. Then, find the composition $$ g(f(x))  by $$substituting $$ f(x) $$ into $$ g(x) . $$Replace every $$ x  in$$ $$ g(x) = \frac{x - 8}{3} $$ with $$ f(x) = 3x + 8 . So$$, write $$ g(f(x)) = \frac{(3x + 8) - 8}{3} . $$Simplify the expression for $$ g(f(x))  by $$performing the subtraction in the numerator and then dividing by 3. Finally, determine whether $$ f $$ and $$ g $$ are inverses by checking if both compositions $$ f(g(x)) $$ and $$ g(f(x)) $$ simplify to $$ x . If $$both equal $$ x $$, then $$ f $$ and $$ g $$ are inverse functions.

Find f(g(x)) and g (f(x)) and determine whether each pair of functions ƒ and g are inverses of each other. f(x)=3x+8 and g(x) = (x-8)/3

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Key Concepts

Function Composition

Inverse Functions

Algebraic Manipulation