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

f(x) = x2 – 2

f(x)
domain: x[tex]\geq 0[/tex], range: y[tex]\geq -2[/tex]
f–1(x)
domain: x[tex]\geq -2[/tex], range: y[tex]\geq 0[/tex]

f(x)
domain: all real numbers, range: y[tex]\geq -2[/tex]
f–1(x)
domain: x[tex]\geq -2[/tex], 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[tex]\leq -2[/tex], range: all real numbers
f–1(x)
domain: all real numbers, range: y=[tex]\leq -2[/tex]

Respuesta :

Answer:

Step-by-step 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:

Option 2. is the correct answer.

Step-by-step 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 [tex]f^{-1}(x)[/tex]

Since f(x) = x² - 2

Then we assume y = x² - 2 to get [tex]f^{-1}(x)[/tex]

x² = y + 2

x = √(y+2)

So [tex]f^{-1}(x)[/tex] = √(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.

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