### Video Transcript

Evaluate π of four minus π₯, given
that π of π₯ is equal to three π₯ plus seven.

What this notation is telling us is
that when we take a function named π and we input π₯, our output is three π₯ plus
seven. We can change our input, that is,
replace π₯ with any number, and weβll get a different output. For example, π of two, we replace
π₯ with two. And our expression becomes three
times two plus seven, which gives us 13.

But we havenβt been given a single
number. Weβre told to evaluate π of four
minus π₯. And so, instead of replacing π₯
with a number like two, weβre actually just going to replace π₯ with our input, with
four minus π₯. And so, π of four minus π₯ becomes
three times four minus π₯ plus seven.

Letβs distribute the parentheses or
expand the brackets. To do so, weβre going to multiply
the three by the four and the three by the negative π₯. Three multiplied by four is 12. And three multiplied by π₯ is three
π₯. So, three multiplied by negative π₯
is negative three π₯. π of four minus π₯ is, therefore,
12 minus three π₯ plus seven. We then collect like terms. 12 plus seven is 19. And so, we see that π of four
minus π₯ is negative three π₯ plus 19.