Question

Let f(x) = 4x - 9 and g(x)= x + 1. Find f(g(x)) and g(f(x))

Answer 1

`\begin{cases} f(x)=4x-9\\\\ g(x)=x+1 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ f(~~g(x)~~)=4[g(x)]-9\implies f(~~g(x)~~)=4[x+1]-9 \\\\\\ f(~~g(x)~~)=4x+4-9\implies \boxed{f(~~g(x)~~)=4x-5} \\\\[-0.35em] ~\dotfill\\\\ g(~~f(x)~~)=[f(x)]+1\implies g(~~f(x)~~)=[4x-9]+1 \\\\\\ g(~~f(x)~~)=4x-9+1\implies \boxed{g(~~f(x)~~)=4x-8}`