Question

What is the domain and range for the following function and its inverse?

f(x) = x2 – 2

f(x)
domain: x
`\geq 0`, range: y
`\geq -2`
f–1(x)
domain: x
`\geq -2`, range: y
`\geq 0`

f(x)
domain: all real numbers, range: y
`\geq -2`
f–1(x)
domain: x
`\geq -2`, range: all real numbers

f(x)
domain: all real numbers, range: all real numbers
f–1(x)
domain: all real numbers, range: all real numbers

f(x)
domain: x
`\leq -2`, range: all real numbers
f–1(x)
domain: all real numbers, range: y=
`\leq -2`

Answer 1

Explanation:

F(X)=2X-2

X=2Y-2

X+2=2Y

(X+2)/2=F-1(X)

FOR BOTH FUNCTIONS DOMAIN AND RANGE ARE ALL REAL NUMBERS

Answer 2

Option 2. is the correct answer.

Explanation:

The given function is f(x) = x² - 2

Therefore the domain of the function f(x) will be (-∞ +∞) or domain: all real numbers

Now range of function f(x) will be [-2,∞) Or y ≥ -2

Now we have get the domain and range of
`f^(-1)(x)`

Since f(x) = x² - 2

Then we assume y = x² - 2 to get
`f^(-1)(x)`

x² = y + 2

x = √(y+2)

So
`f^(-1)(x)` = √(x+2)

Now the domain of x ≥ -2 because function is not defined for the values of x < -2

Range of the function will be all real numbers.