Evaluate 𝑓 of four minus 𝑥, given
that 𝑓 of 𝑥 is equal to three 𝑥 plus seven.
What this notation is telling us is
that when we take a function named 𝑓 and we input 𝑥, our output is three 𝑥 plus
seven. We can change our input, that is,
replace 𝑥 with any number, and we’ll get a different output. For example, 𝑓 of two, we replace
𝑥 with two. And our expression becomes three
times two plus seven, which gives us 13.
But we haven’t been given a single
number. We’re told to evaluate 𝑓 of four
minus 𝑥. And so, instead of replacing 𝑥
with a number like two, we’re actually just going to replace 𝑥 with our input, with
four minus 𝑥. And so, 𝑓 of four minus 𝑥 becomes
three times four minus 𝑥 plus seven.
Let’s distribute the parentheses or
expand the brackets. To do so, we’re going to multiply
the three by the four and the three by the negative 𝑥. Three multiplied by four is 12. And three multiplied by 𝑥 is three
𝑥. So, three multiplied by negative 𝑥
is negative three 𝑥. 𝑓 of four minus 𝑥 is, therefore,
12 minus three 𝑥 plus seven. We then collect like terms. 12 plus seven is 19. And so, we see that 𝑓 of four
minus 𝑥 is negative three 𝑥 plus 19.