In Exercises 75-82, express the given function h as a composition...

Question

In Exercises 75-82, express the given function h as a composition of two functions ƒ and g so that h(x) = (fog) (x). h(x) = |2x-5|

Accepted Answer

Welcome back. I'm so glad you're here. We have the function H of X and we are told H of X is the absolute value of three X minus seven. And we're told that H of X is equal to a composite function F of G of X. And we are asked to find F of X and G of X. So let's first think about in a composite function. What goes inside of what so for F of G of X or fog X, what goes inside of what the G of X goes inside of the F of X. So now we want to take a look at our known function R. H of X and see what operations are happening to the X value here. It's being multiplied by 3 1st and then it's having seven subtracted from it. And then the last operation happening to it is the absolute value of it is being taken. And when we put the G of X inside the F of X, the f of X is what's going to be happening to it last because it's on the outside. So the last thing happening to our X is the absolute value of it being taken. So for F of X that is equal to the absolute value of X. And then G of X is going to go inside of our F of X function. So our G of X is going to be all the other operations happening to X here. So G of X is going to be three X minus seven and we can check this. So for our composite function F of G of X, we're going to start writing our F of X function and we're going to stop as soon as we hit an X. So we'll write the absolute value line and then we've already hit an X. And now we substitute G of X in for X. So instead of the absolute value of X as the absolute value of three X minus seven. And then we finish writing our F. Of X function. And yes this matches this equals R. H. Of X. Yay. So we've correctly determined our F. Of X and our G of X. We look at our answer choices and this matches with answer choice C. Well done. We'll catch you on the next one.

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In Exercises 75-82, express the given function h as a composition of two functions ƒ and g so that h(x) = (fog) (x). h(x) = |2x-5|