Find p(-2) and p(3) for each function : P(x)= -7x^2+5x+9

Question

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  If f(x)=x^2, g(x)= 5x, h(x)=x+4 find each value

        F[g(1)]

         h[f(20)]

         h[g(-3)]

        h[f(4)]

Answer 1

Hi, Megan!

 

These are called "composite" functions, and you treat them like a chain reaction. Let's look at the first one.

 

f[g(1)]

 

It looks like it's telling us to stick something into the f function. For example, if you saw just f(1), you'd put 1 in for x in the f function...and you'd get f(1) = 1² = 1. But what are we sticking into the f function? There's that g in there...hmm.

 

Let's start from the inside, because we know what to do there. The inside is g(1). So put 1 in for x in the g function.

 

g(1) = 5(1) = 5.

 

Putting this in our question of f[g(1)], we now have f[5]. We can do that! So let's put 5 in for x in the f function:

 

f(5) = 5² = 25. There's our answer!

 

Let's look at the second. h[f(20)].

 

We look from the inside out, because that's where the number is. Without a number to put in for x, we can't go anywhere with this. So let's start with the number, 20. Next to the 20 we see the f. So first we'll put 20 in for x in the f function.

 

f(20) = 20² = 400

 

Now we have h[400].

 

h[400] = 400 + 4 = 404. That's the answer.

 

The most common mistake with these is to put the number in the wrong function first. ALWAYS start with the function closest to the number. So in the third one, h[g(-3)], start by putting the -3 in for x in the g function. Work from the inside out. Once you get the solution for the g function, take that answer and put it into the h function.

 

Hope this helps!!