Question 624932
Problems like this are alot easier once you learn to understand what something like:
f(x) = 4x + 9
is telling you. The expression inside the parentheses following a function name is the input to the function. The "x" here is simply a place-holder for whatever input you choose to put into function f. The right side of the equation tells us what this particular function f will do with its input. It tells us that f will take the input, multiply it by 4 and then add 9. It will do this for <i>any</i> input to f, not just an input of x. In summary, f(x) = 4x + 9 tells us that f will multiply <i>any</i> input by 4 and then add 9.<br>
Once we get this idea, it is a lot easier to see how to handle:
f(g(x))
which says that g(x) is the input being put into function f. And what does f do with <i>any</i> input? It multiplies it by 4 and adds 9! So
f(g(x) = 4(g(x)) + 9
Since g(x) = -5x + 7 this becomes:
f(g(x)) = 4(-5x + 7) + 9
which simplifies as follows:
f(g(x)) = -20x + 28 + 9
f(g(x)) = -20x + 37<br>
Some other examples:
f(q) = 4q+9
f(2x) = 4(2x) + 9 = 8x + 9
{{{f(x^2) = 4x^2 + 9}}}
f(x+6) = 4(x+6) + 9 = 4x + 24 + 9 = 4x + 33
etc.