The correct answer is option D. Which is the even function is f (x) = x⁴.
What is an even function?
The function in which when the sign of the input variable is changed the output remains the same is called the even function. Mathematically we can write it as f(x) = f(-x ).
let us check the given four options:-
A f(x) = √x ; f(-x) = √-x here f(x) ≠ f(-x)
B f(x) = x ; f(-x) = -x here f(x) ≠ f(-x)
C f(x) = x³ + 1 ; f(-x) = -x³ + 1 here f(x) ≠ f(-x)
D f(x) = x⁴ ; f(-x) = (-x)⁴ = x⁴ here f(x) = f(-x)
We can see that in the option D the f(x) = x⁴ is an even function because f(x) = f(-x).
Therefore the correct answer is option D. Which is the even function is f (x) = x⁴.
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