Question

What is the value of g[f(3)] for the functions f(x) = 2x+3 and g(x) = x + 1

Answer 1

Given functions are:

`\begin{gathered} f\mleft(x\mright)=2x+3 \\ g\mleft(x\mright)=x+1 \end{gathered}`

First find g[f(x)]:

`\begin{gathered} g\lbrack f(x)\rbrack=(2x+3)+1 \\ g\lbrack f(x)\rbrack=2x+4 \end{gathered}`

Nut put x=3 in above equation:

`\begin{gathered} g\lbrack f(3)\rbrack=2(3)+4 \\ g\lbrack f(3)\rbrack=6+4 \\ g\lbrack f(3)\rbrack=10 \end{gathered}`