Question

2f: x H x2 + 4x for xe R, x>-2
a State the domain and range of f-
b Find an expression for f-'(x).​

Answer 1

Answer:

x H x2 + 4x for xe R, x>-2

a State the domain and range of f-

b Find an expression for f-'(x).

Answer 2

Given : f(x) = x² + 4x   x ∈ R  , x > - 2

To Find :  Domain and Range  of F(x)

Domain and Range  of f⁻¹(x)

expression for f⁻¹(x)

Solution:

f(x) = x² + 4x   x ∈ R  , x > - 2

Domain = (-2 , ∞ )

f(x) = x² + 4x

f'(x) = 2x + 4

x > - 2

=> f'(x) > 0 Hence strictly increasing function in  (-2 , ∞ )

at x = - 2

f(x) = x² + 4x  = 4 - 8 = - 4

Range = ( - 4 ,  ∞ )

For f⁻¹(x) , domain and range will get interchanged

Domain =  ( - 4 ,  ∞ )

Range = (-2 , ∞ )

f(y) = y² + 4y

=> x =  y² + 4y

=> x + 4 =  y² + 4y + 4

=> x + 4  = (y + 2)²

=> √x + 4  = y + 2

=> y = √x + 4 - 2

expression for f⁻¹(x) = √(x + 4)  -  2   x > - 4

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