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

Evaluate 𝑓(4 βˆ’ π‘₯), given that 𝑓(π‘₯) = 3π‘₯ + 7.


Video Transcript

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

What this notation is telling us is that when we take a function named 𝑓 and we input π‘₯, our output is three π‘₯ plus seven. We can change our input, that is, replace π‘₯ with any number, and we’ll get a different output. For example, 𝑓 of two, we replace π‘₯ 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 π‘₯. And so, instead of replacing π‘₯ with a number like two, we’re actually just going to replace π‘₯ with our input, with four minus π‘₯. And so, 𝑓 of four minus π‘₯ becomes three times four minus π‘₯ 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 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‘₯. 𝑓 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 𝑓 of four minus π‘₯ is negative three π‘₯ plus 19.

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