Math Help - Composite Functions

1. Composite Functions

For this question: find gof:
f: R ---> R and g: R ---> R given by f(x) = 2x -5 and g(x) = 5x +2

I've done my working out and would like to know if this is correct.

(fog)(x) = f(5x+2)
(fog)(x) = 2(5x+2)-5
(fog)(x) = 10x+4-5
(fog)(x) = 10x-1

Is that all I need to do for this question and is what I've done right?
The R's obviously mean real numbers.

2. Hello, brumby_3!

You found the wrong composite . . .

$f\!:\! R \to R\:\text{ and }\:g\!:\! R \to R$

. . given by: . $\begin{array}{ccc}f(x)& =&2x -5 \\g(x) &= &5x +2\end{array}$

Find ${\color{red}g\circ f}$

$g\circ f \;=\;g(f(x))$

. . . . $=\;g(2x-5)$

. . . . $=\;5(2x-5) + 2$

. . . . $=\;10x-25+2$

. . . . $=\; 10x - 23$