Question

9. Mario found the composite function (hºg)(x), where h(x) = 4 -

- ž, and g(x) = 2x + 10.
State which step he made the error and explain the mistake he made in his reasoning,
(2x + 10)
Step 1: h(g(x)) = 4 -
2
Step 2: h(g(x)) = 4 - x + 10
Step 3: h(g(x)) = 14 - X
a. Step 1: 2(4 - Ž)+10
b. Step 2: h(g(x)) = 4 - x + 5
c. Step 2: h(g(x)) = 4 - x-5
d. no error

Answer 1

The mistake is in step 2

Explanation:

We are given h(x)=4-x

Note: Considering h(x)=4-x as in question given there is some issue. If value of h(x) is different the answer would be different.

and g(x)=2x+10

We need to find h(g(x))

h(g(x)) can be found by putting the value of g(x) in h(x)

Steps used by Mario are:

Step 1: h(g(x)) = 4 - x

Step 2: h(g(x)) = 4 - x + 10

Step 3: h(g(x)) = 14 - X

She did mistake in step 2:

The step 2 should be:

h(g(x))=4-(2x+10)

h(g(x))= 4-2x-10

h(g(x))=-6-2x

So, the mistake is in step 2