## f(x)=(x^4)+7x^2+5

### Let’s take a look at the function f(x) = x^4 + 7x^2 + 5

Let’s take a look at the function f(x) = x^4 + 7x^2 + 5.

1. What is a function?

In mathematics, a function is a relation that assigns a unique output value for every input value. In simpler terms, it is a rule that takes an input and produces a corresponding output.

2. How can we evaluate the function f(x) = x^4 + 7x^2 + 5?

To evaluate the function, you substitute the value of x into the expression for f(x). Let’s say we want to evaluate f(x) at x = 3. We would substitute 3 into the expression:

f(3) = (3^4) + 7(3^2) + 5

= 81 + 7(9) + 5

= 81 + 63 + 5

= 149

Therefore, f(3) = 149.

3. What is the domain of the function f(x) = x^4 + 7x^2 + 5?

The domain of a function is the set of all possible input values for which the function is defined. In this case, since f(x) is a polynomial function, there are no restrictions on the domain. Hence, the domain of f(x) is all real numbers, or (-∞, ∞).

4. What is the range of the function f(x) = x^4 + 7x^2 + 5?

The range of a function is the set of all possible output values. In this case, since the function is a fourth-degree polynomial, the range is also all real numbers, or (-∞, ∞).

5. What are the x-intercepts of the function f(x) = x^4 + 7x^2 + 5?

The x-intercepts are the values of x for which the function equals zero. To find them, we set f(x) equal to zero and solve for x:

x^4 + 7x^2 + 5 = 0

Unfortunately, there is no simple algebraic solution for this equation. However, you can find the x-intercepts using numerical methods or graphing software.

These are the main concepts related to the given function. If you have any further questions or need clarification about any of these concepts, feel free to ask!

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