Question

Function: g(x)=2x^2-8.
For x > 0, the inverse is f(x)=sqrt 1/2x+4.
For x < 0, the inverse function is d(x)= -sqrt 1/2x+4.
x: -8, 0, 10.
f(x): 0, r, s.
d(x): q, -2, t.
q=?
r=?
s=?
t=?

Answer 1

The values of q, r, s, and t are:

• 0
• 2
• 3
• -3

Calculations and Parameters

The given function is $g(x) = 2x^2 - 8$

The inverse of g(x) for x ≥ 0 is $f(x) = \sqrt{\frac{1}{2}x+4}$

The inverse of g(x) for x ≤ 0 is $d(x) = -\sqrt{\frac{1}{2}x + 4}$

For x= -8

d(-8)= $-\sqrt{\frac{1}{2} (-8) + 4}$

q= d(-8) = 0

r= f(0)

f(x) = $\sqrt{\frac{1}{2}x + 4 } \\\sqrt{\frac{1}{2} (0) +4 }$

f(0)= \sqrt 4

f(0)= 2

r= 2

f(10)= \sqt 9

s= 3

t= d(10)

d(10)= -\sqrt9

t= -3

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