find f(g(x)) and g(f(x)). then determine whether g and f are inverse functions. f(x)=10x - 8 g(x)=0.1x + 0.8…
find f(g(x)) and g(f(x)). then determine whether g and f are inverse functions. f(x)=10x - 8 g(x)=0.1x + 0.8 f(g(x))=
Answer
Explanation:
Step1: Substitute g(x) into f(x)
$f(g(x))=10(0.1x + 0.8)-8$
Step2: Expand the expression
$f(g(x))=10\times0.1x+10\times0.8 - 8$ $f(g(x))=x + 8-8$
Step3: Simplify the expression
$f(g(x))=x$
Step4: Substitute f(x) into g(x)
$g(f(x))=0.1(10x - 8)+0.8$
Step5: Expand the expression
$g(f(x))=0.1\times10x-0.1\times8 + 0.8$ $g(f(x))=x-0.8 + 0.8$
Step6: Simplify the expression
$g(f(x))=x$
Since $f(g(x)) = x$ and $g(f(x))=x$, the functions $f$ and $g$ are inverse functions.
Answer:
$f(g(x))=x$; $g(f(x))=x$; $f$ and $g$ are inverse functions.