Question

far the pair of functions f(x)=3, and g(x)=4^2-3x+1

a: (f*g)(x)
b: (f*g)(2)
c: (g*f)(x)
d: (g*f)(-4)

Help me solve all of these I am stuck & Idk how to get the answers

Answer 1

Now, let's be sure: the problem has \((f*g)(x), \text { NOT } (f\circ g)(x)\), correct?
If that is correct, then:
\[(f*g)(x) = f(x)*g(x) =\]
\[(f*g)(2) = f(2)*g(2) = \]
\[(g*f)(x) = g(x)*f(x) = \]
\[(g*f)(-4) = g(-4)*f(-4) = \]

Answer 2

No the porblem has (f∘g)(x.. i Just assumed that lil circle was a *

Answer 3

Okay, I'm glad I asked, that means something different!

\[(f\circ g)(x)\]means take the right hand side of \(g(x) = 4x^2-3x+1\) and substitute that whole thing wherever you see \(x\) in the right hand side of \(f(x)\). For the first two, you'll undoubtedly notice that \(x\) doesn't appear in the right hand side of the definition of \(f(x)\) which makes the first two quite simple.

by the way, is \(g(x) = 4x^2-3x+1\) as I assumed, or is it really \(g(x) = 4^2-3x+1\) as you wrote?

Answer 4

yes

Answer 5

yes isn't a valid answer to that question :-)

Answer 6

or it is valid, but isn't helpful :-)

Answer 7

wait so whats the answer

Answer 8

SO the answer to a would be
a. \[f(g(x))=f(4x^2-3x+1)=3\]

b. \[f(g(2))=f(4*4-3*2+1)=f(11)=3\]

c. \[g(f(x))=g(3)=4(3)^2-3(3)+1=28\]

d. \[g(f(-4))=g(3)=28\]