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

Evaluate 𝑓(4 − 𝑥), given that 𝑓(𝑥) = 3𝑥 + 7.

01:26

### Video Transcript

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.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.