Quiz about QUIZ TOPIC 5

Question 1

Based on the diagram, state the domain and range of $$f$$ .

Accepted Answer

$$D_f=\left(-\infty,\infty\right),\ R_f=\left(-\infty,0\right]$$

Answer

$$D_f=\left(-2,\infty\right),\ R_f=\left(-\infty,1\right]$$

Answer

$$D_f=\left(-\infty,\infty\right),\ R_f=\left[-2,1\right]$$

Answer

$$D_f=\left(-\infty,1\right),\ R_f=\left(-2,\propto\right)$$

Question 2

Given $$f\left(x\right)=\sqrt[]{x-2}$$ and $$g\left(x\right)=1-2x$$ . Find $$\left(f\circ g\right)\left(x\right)$$ .

Accepted Answer

$$\sqrt[]{-2x-1}$$

Answer

$$1-2\sqrt[]{x-2}$$

Answer

$$\sqrt[]{2x+1}$$

Answer

$$2-\sqrt[]{x-2}$$

Question 3

Find $$f\left(x\right)$$ if $$\left(f\circ g\right)\left(x\right)=x^2+1$$ and $$g\left(x\right)=x+3$$ .

Accepted Answer

$$x^2-6x+10$$

Answer

$$x^2-2$$

Answer

$$4x^2+4x+1$$

Answer

$$x^2$$

Question 4

Given $$\left(g\circ f\right)\left(x\right)=3x^2$$ and $$g\left(x\right)=3e^x$$ . Find $$f\left(x\right)$$ .

Accepted Answer

$$2\ln x$$

Answer

$$e^{3x+2}$$

Answer

$$e^x$$

Answer

$$2\left(\ln3+x\right)$$

Question 5

What can we say if $$fg\left(x\right)=x$$ ?

Accepted Answer

All of the above

Answer

$$f$$ and $$g$$ are inverses of each other.

Answer

$$f$$ is the inverse of $$g$$

Answer

$$g$$ is the inverse of $$f$$

Question 6

Determine the quotient and remainder when a polynomial $$2x^3-3x^2-4x+1$$ divided by $$x-4$$ .

Accepted Answer

$$Q\left(x\right)=2x^2+5x+16,\ R\left(x\right)=65$$

Answer

$$Q\left(x\right)=x^2+5x+6,\ R\left(x\right)=46$$

Answer

$$Q\left(x\right)=x^2+4x-5,\ R\left(x\right)=30$$

Answer

$$Q\left(x\right)=x^2+6x+5,\ R\left(x\right)=52$$

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