Question

18: Assume f(x) = -2x + 8 and g(x) = 3x , what is the value of (g o f)(3)?

A: 6
B: x + 8
C: -10
D: 23

19: None

20: Let h(x) = (g o f)(x) = x^2/ x^2 + 1
Which of the following could be a possible decomposition of h(x)?

A: F(x) = x^2 ; g(x) = x
-------
x + 1

B: f(x) = x + 1; g(x) = x^2

C: f(x) = x + 1; g(x) = 1
-----
x^2

D: f(x) = x ;g(x) = x
-------
x + 1

Answer 1

QUESTION №18

Assume $f(x)=-2x+8$ and $g(x)=3x$, what is the value of $(gof)(3)$ ?

$A:$ $6$

$B:$ $x+8$

$C:$ $-10$

$D:$ $23$

SOLUTION

$(gof)(x)=g\left(f(x)\right)=g(-2x+8)=3(-2x+8)=-6x+24$

$(gof)(3)=\left.(-6x+24)\right|_{x=3}=24-6*3=24-18=6$

ANSWER

$(gof)(3)=6$

A:6

QUESTION №20

Let $h(x)=(gof)(x)=\frac{x^{2}}{x^{2}+1}$

Which of the following could be a possible decomposition of $h(x)$?

$A:$ $f(x)=x^{2};\ g(x)=\frac{x}{x+1}$

$B:$ $f(x)=x+1;\ g(x)=x^{2}$

$C:$ $f(x)=x+1;\ g(x)=\frac{1}{x^{2}}$

$D:$ $f(x)=x;\ g(x)=\frac{x}{x+1}$

SOLUTION

$h(x)=(gof)(x)=g\left(f(x)\right)=\frac{x^{2}}{x^{2}+1}$

Iterate through all the options one by one

$A:$ $f(x)=x^{2};\ g(x)=\frac{x}{x+1}$

$h(x)=g(f(x))=g(x^{2})=\frac{x^{2}}{x^{2}+1}$

$$B: \quad f(x) = x + 1; \; g(x) = x^2$$ $$h(x) = g(f(x)) = g(x + 1) = (x + 1)^2$$ $$C: \quad f(x) = x + 1; \; g(x) = \frac{1}{x^2}$$ $$h(x) = g(f(x)) = g(x + 1) = \frac{1}{(x + 1)^2}$$ $$D: \quad f(x) = x; \; g(x) = \frac{x}{x + 1}$$ $$h(x) = g(f(x)) = g(x) = \frac{x}{x + 1}$$

ANSWER

$$A: \quad f(x) = x^2; \; g(x) = \frac{x}{x + 1}$$

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