The correct answer is option D. Which is the even function is f (x) = x⁴.
<h3>What is an even function?</h3>
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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Answer:
<em>The domain of f is (-∞,4)</em>
Step-by-step explanation:
<u>Domain of a Function</u>
The domain of a function f is the set of all the values that the input variable can take so the function exists.
We are given the function
It's a rational function which denominator cannot be 0. In the denominator, there is a square root whose radicand cannot be negative, that is, 4-x must be positive or zero, but the previous restriction takes out 0 from the domain, thus:
4 - x > 0
Subtracting 4:
- x > -4
Multiplying by -1 and swapping the inequality sign:
x < 4
Thus the domain of f is (-∞,4)
Answer:
828382772
Step-by-step explanation:
do it your self
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