Question

Let f(x) = 4x - 7 and g(x) = x +5. Find f(g(x)) and g(f(x)).

f(g(x)) = (Simplify your answer.)
g(f(x)) = (Simplify your answer.)

Answer 1

`\huge \bf༆ ᴀɴsweʀ ༄`

Here's the solution ~

The given expressions are :

`\qquad \sf \: f(x) = 4x - 7`

`\qquad \sf \: g(x) = x +5`

1. Now, let's solve for ~ f (g( x )) = ?

`\qquad \sf  \dashrightarrow \: f(x) = 4x - 7`

`\qquad \sf  \dashrightarrow \: f(g(x) )= 4(x + 5)- 7`

`\qquad \sf  \dashrightarrow \: f(g(x) )= 4x + 20- 7`

`\qquad \sf  \dashrightarrow \: f(g(x) )= 4x + 13`

2. solve for g(f( x )) = ?

`\qquad \sf  \dashrightarrow \: g(x) = x +5`

`\qquad \sf  \dashrightarrow \: g(f(x)) = 4x - 7+5`

`\qquad \sf  \dashrightarrow \: g(f(x)) = 4x - 2`