Question

METAL WILL BE REWARDED
1.Let f(x) = -4x + 7 and g(x) = 10x - 6, find f(g(x))

2.Let f(x) = 5x + 12. Find f-1(x)

Answer 1

\(\bf f(x) = -4x + 7 \qquad {\color{red}{ g(x)}} = 10x - 6
\\ \quad \\
f(\quad {\color{red}{ g(x)}}\quad )=-4{\color{red}{ x}} + 7\implies f(\quad {\color{red}{ g(x)}}\quad )=-4({\color{red}{ 10x - 6}}) + 7\\
---------------------------\\


f(x) = {\color{red}{ y}}=5{\color{blue}{ x}} + 12\implies {\color{blue}{ x}}=5{\color{red}{ y}} + 12\quad \textit{solve for "y"}\)

as you can see, to get the inverse "relation", we simply swap about the variables, and then just solve for "y" to get \(\bf f^{-1}(x)\)