Question

Suppose that the functions f and g are defined for all real numbers x as follows.

f(x) = 3x+3
g(x) = 5x
Write the expressions for (f times g)(x) and (f+g)(x) and evaluate (f-g)(2)

Answer 1

solution given:

f(x) = 3x+3

g(x) = 5x

now

(f times g)(x)=?

(f+g)=?

(f-g)=?

we have

(f times g)(x)=f(g(x))

substituting value of g(x)

f(g(x))=f(5x)

now replacing value of x in f(x)

f(5x)=3(5x)+3

solving it

f(5x)=15x+3

so (f times g)(x) =15x+3

Explanation:

again,

(f+g)(x)=f(x)+g(x)=3x+3+5x=8x+3

so

(f+g)(x) =8x+3

again

we need to find (f-g)(x) first so

(f-g)(x)=f(x)-g(x)=3x+3-5x=-2x+3

now

(f-g)(2)=-2*2+3=-1

(f-g)(2)=-1

Answer 2

Explanation:

a) fg(x)

--> f(5x)

--> 3(5x)+3

--> 15x+3

b) f+g(x)

--> 3x+3+ 5x

c) (f-g)(2)

3x+3- 5x

--> 3(2)+3-5(2)

--> -1