Question

Can somebody please help/guide me through 2 of these questions?

1. For which pair of functions is (g of x)(a)= lal-2?
A. f(a)=a^2-4 and g(a)= square root of a
B. f(a)=1/2a-1 and g(a)=2a-2
C. f (a)=5+a^2 and g(a)= square root of a-5-2
D. f(a)=3-3a and g(a)=4a-5

2. Let f(x) be a polynomial function of degree 2 and g(x) be a polynomial function of degree 3. What is the degree of (f of g)(x)?
A.2
B.3
C.5
D.6

I got 6 is that correct?

Answer 1

For the 2 question, do you mean
What is the degree of (f o g)(x)? (not f of g)(x)

f o g means replace x in f with g(x)
g(x) is polynomial of degree 3. example x^3 + x^2 + x +1
f(x) is degree 2. example x^2 + x + 1

when we put g(x) in for x in f(x) we get this mess
(x^3 + x^2 + x +1)^2 + (x^3 + x^2 + x +1) + 1

but luckily all we care about is the highest exponent, which will come from x^3 * x^3 = x^6

so yes, 6 is the answer.

Answer 2

thank you! and yes that's what I meant.

Answer 3

did you try Q1?

Answer 4

Nope :(

Answer 5

(g o f)(a) means replace all "a" s in g with f(a)

test the choices.
write down g(a): g= sqr(a)
replace "a" with f(a): sqr(a^2-4)
a^2 -4 is not a perfect square... it factors into (a-2)(a+2) so that is not the answer

can you try the second choice?

Answer 6

It's C.

Answer 7

yes, I think so, but it depends on what
g(a)= square root of a-5-2
means

if it means
\[ g(a) = \sqrt{a-5} - 2 \]
then when we replace a with f(a) = 5+a^2 we get
\[ g(a) = \sqrt{5+a^2-5} - 2 \\= \sqrt{a^2} - 2 = a-2\]
because we take the positive root, we should write it as |a| - 2

Answer 8

Thanks! :)

Answer 9

yw