# 微积分网课代修|预备微积分代写precalculus辅导|MTH-175 Finding Input and Output Values of a Function

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## 微积分网课代修|预备微积分代写precalculus辅导|Finding Input and Output Values of a Function

When we know an input value and want to determine the corresponding output value for a function, we evaluate the function. Evaluating will always produce one result because each input value of a function corresponds to exactly one output value.

When we know an output value and want to determine the input values that would produce that output value, set the output equal to the function’s formula and solve for the input. Solving can produce more than one solution because different input values can produce the same output value.

## 微积分网课代修|预备微积分代写precalculus辅导|Evaluation of Functions in Algebraic Forms

When we have a function in formula form, it is usually a simple matter to evaluate the function. For example, the function $f(x)=5-3 x^{2}$ can be evaluated by squaring the input value, multiplying by 3 , and then subtracting the product from $5 .$
How To…
Given the formula for a function, evaluate.

Replace the input variable in the formula with the value provided.

Calculate the result.
Example 6 Evaluating Functions at Specific Values
Evaluate $f(x)=x^{2}+3 x-4$ at:
a. 2
b. $a$
c. $a+h$
d. $\frac{f(a+h)-f(a)}{h}$
Solution Replace the $x$ in the function with each specified value.
a. Because the input value is a number, 2, we can use simple algebra to simplify.
\begin{aligned} f(2) &=2^{2}+3(2)-4 \ &=4+6-4 \ &=6 \end{aligned}
b. In this case, the input value is a letter so we cannot simplify the answer any further.
$$f(a)=a^{2}+3 a-4$$
c. With an input value of $a+h$, we must use the distributive property.
\begin{aligned} f(a+h) &=(a+h)^{2}+3(a+h)-4 \ &=a^{2}+2 a h+h^{2}+3 a+3 h-4 \end{aligned}

## 微积分网课代修|预备微积分代写precalculus辅导|Evaluation of Functions in Algebraic Forms

Evaluate $f(x)=x^{2}+3 x-4$ 在:

C。 $a+h$
d。 $\frac{f(a+h)-f(a)}{h}$

$$f(2)=2^{2}+3(2)-4 \quad=4+6-4=6$$

$$f(a)=a^{2}+3 a-4$$
C。输入值为 $a+h$ ，我们必须使用分配属性。
$$f(a+h)=(a+h)^{2}+3(a+h)-4 \quad=a^{2}+2 a h+h^{2}+3 a+3 h-4$$