The figure shows the graph of a function f (x)
which is a semi-circle centred at origin.
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Given : The figure shows the graph of a function f (x) is a semi-circle centred at origin.
To Find :
Solution:
Equation of circle center at origin and radius 4
x² + y² = 4²
=> y² = 4² - x²
=> y = √4² - x² ( only + ve values of y as semicircle is above x axis )
f(x) = √4² - x²
4² - x² ≥ 0
=> x² ≤ 4²
=> -4 ≤ x ≤ 4
Domain of x = [-4 , 4]
x ∈ [-4 , 4]
Range of f(x) = [0 , 4]
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