Consider the function ℎ of 𝑥 equals three minus 𝑥 over seven, which is defined for all values of 𝑥. Work out the inverse of ℎ of 𝑥.
The first thing we’re gonna do here is write 𝑦 in place of ℎ of 𝑥. So we have the range 𝑦 equals three minus 𝑥 over seven. And we want to turn this 𝑦 equals three minus 𝑥 over seven into some function of 𝑥. We want it to say 𝑥 equals something.
We want to know how 𝑥 is related to 𝑦. We can multiply both sides of the equation by seven over one. On the right, the sevens cancel out, leaving us with three minus 𝑥. And on the left, seven times 𝑦 equals seven 𝑦.
From there, we can add 𝑥 to both sides of the equation. 𝑥 plus seven 𝑦 equals three. Then subtract seven 𝑦 from both sides. And 𝑥 equals three minus seven 𝑦. We’ll use this three minus seven 𝑦 to create our inverse function. The inverse of ℎ of 𝑥 equals three minus seven 𝑥. In order to find the inverse, we need to switch the 𝑥 and 𝑦. And our inverse function will be three minus seven 𝑥.