Question

F(x) = 3x3 + 8x2 - 7x - 4

g(x) = 2x – 6
Find (f - g)(x).
--
5x + 2
92 + 2
1
A. (f - g)(x) = 3x3 + 8x2
B. (f - g)(x) = 3x3 + 8x2
c. (f - g)(x) = 3x3 + 8x2
D. (f - g)(x) = 3x3 + 8x2
-
9x
10
52
10

Answer 1

`B)f^(-1)(x)=\sqrt[3]{(x+4)/(3)}`

Step-by-step explanation

`f(x)=3x^3-4`

Step 1

swap the variables x and y

`\begin{gathered} f(x)=3x^3-4 \\ y=3x^3-4 \\ y=3x^3-4\rightarrow x=3y^3-4 \\ x=3y^3-4 \end{gathered}`

Step 2

now, isolate y

`\begin{gathered} x=3y^3-4 \\ \text{add 4 in both sides} \\ x+4=3y^3-4+4 \\ x+4=3y^3 \\ \text{divide both sides by 3} \\ (x+4)/(3)=(3y^3)/(3) \\ (x+4)/(3)=y^3 \\ \text{get the cubic root in both sides} \\ \sqrt[3]{(x+4)/(3)}=\sqrt[3]{y^3} \\ \sqrt[3]{(x+4)/(3)}=y\rightarrow inverse\text{ function} \end{gathered}`

therefore, the answer is

`B)f^(-1)(x)=\sqrt[3]{(x+4)/(3)}`

I hope this helps you