# Question Video: Evaluating Linear Function at a Specific Value Mathematics • 8th Grade

Evaluate π(4 β π₯), given that π(π₯) = 3π₯ + 7.

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### 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 weβll 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 havenβt been given a single number. Weβre told to evaluate π of four minus π₯. And so, instead of replacing π₯ with a number like two, weβre 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.

Letβs distribute the parentheses or expand the brackets. To do so, weβre 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.