Which of the following describes a true relationship between the functions f x - x-3 2 -2 and g x - 1 2 x-1 graphed below in the standard x-y coordinate plane-

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f(x) Transforms to |f(x)|

Which of the ...

Question

Which of the following describes a true relationship between the functions $f (x) = {(x - 3)}^{2} + 2$ and $g (x) = \frac{1}{2} x + 1$ graphed below in the standard $(x, y)$ coordinate plane?

f (x) = g (x)

for exactly

2

values of

x

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f (x) = g (x)

for exactly

1

values of

x

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f (x) < g (x)

for all

x

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f (x) > g (x)

for all

x

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f (x)

is the inverse of

g (x)

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Solution

The correct option is B $f (x) = g (x)$ for exactly $2$ values of $x$
Given $f (x) = {(x - 3)}^{2} + 2, g (x) = \frac{x}{2} + 1$
$f (x) - g (x) = {(x - 3)}^{2} + 2 - \frac{x}{2} - 1$
$= x^{2} - 6 x + 9 + 1 - \frac{x}{2}$
$= x^{2} - \frac{13 x}{2} + 10$
$= {(x - \frac{13}{4})}^{2} - \frac{9}{16}$
$∴ f (x) - g (x) = 0$ for exactly two values of x
$∴ f (x) = g (x)$ for exactly two values of x.

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How many of the following pairs of function are identcal

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(b) $f (x) = \frac{x^{2} - 1}{x - 1}, g (x) = x + 1$

(d) $f (x) = \frac{x}{x^{2}}, g (x) = \frac{1}{x}$

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Which of the following describes a true relationship between the functions f(x)=(x−3)2+2 and g(x)=12x+1 graphed below in the standard (x,y) coordinate plane?

The correct option is B f(x)=g(x) for exactly 2 values of xGiven f(x)=(x−3)2+2,g(x)=x2+1f(x)−g(x)=(x−3)2+2−x2−1=x2−6x+9+1−x2=x2−13x2+10=(x−134)2−916∴f(x)−g(x)=0 for exactly two values of x∴f(x)=g(x) for exactly two values of x.

Which of the following describes a true relationship between the functions $f (x) = {(x - 3)}^{2} + 2$ and $g (x) = \frac{1}{2} x + 1$ graphed below in the standard $(x, y)$ coordinate plane?