Welcome to the forum.

That's a lot of similar questions, so, hopefully, once you've done one ok, you'll manage the rest on your own.

Think of a function as a box with a number that goes into the box and another number comes out.

Q1. f(x) = 15x – 12 and g(x) = -15x2 + 14x - 10

find g(f(7))

This means put 7 through an 'f' box and then the answer through a 'g' box.

So do 15 times 7 - 12; get an answer and apply the g function to that answer.

Q4. g[f(x)] if g(x) = x2 and f(x) = x + 3.

Same as with numbers but you have to maintain the algebra in going from step one to step two.

So if you put x into the 'f' box, x + 3 comes out. Now put that into the 'g' box (which squares the input)

and (x + 3)^2 will come out.

For some you might need to do some algebraic simplifying, but I don't think this one needs that.

As any number can have 3 added and any number can be squared the domain can be all real numbers.

Please have a try at these and, if you want, you may post your answers back for checking.

Bob

]]>1. f(x) = 15x – 12 and g(x) = -15x2 + 14x - 10

find g(f(7))

2. f(x) = -13x2 - 13x + 14 and g(x) = -13x - 11

find g(g(3))

3. f(x) = 15x + 12 and g(x) = -10x2 + 15

find f(g(-2))

B. Find the composition of functions indicated and state the domain of the composite function showing the work.

4. g[f(x)] if g(x) = x2 and f(x) = x + 3.

5. f[g(x)] if f(x) = 4x + 1 and g(x) = 2x2 - 5

6. g[f(x)] if g(x)=√(x) and f(x)= x + 1

7. h[s(x)] if s(x) = 2x and h(x) = x2

8. f(g(x)) if g(x) = 3/(x - 1), f(x) = x - 1

C. Application Problem

You go to a local mechanic to get your tires changed. The tires cost x dollars. There is a 6% sales tax, but you get a 10% discount.

9. Write a function, t(x) for the total purchase amount after taxes but before discounts and fees.

A t(x)=1.06x

B t(x)=6 + x

C t(x)=x + .06

D t(x)=6x

E t(x)=.06x

F t(x)=x + 6x

10. Write a function, d(x) to account for the total after discounts on purchase amount x but before taxes and fees.

A d(x)=x - 10

B d(x)=x - .10x

C d(x)=x/.10x

D d(x)=x + 10x

E d(x)=x + .10

F d(x)=x - 10x

11. Does it make a difference in the total price whether the mechanic adds the tax first d(t(x)) or takes the discount first t(d(x))? Do not replace x with a numerical value. Show the work to support your answer while keeping x in your work.

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