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1.2.3 Homework

Follow all directions and show all work for credit.

57. If [tex]f(x) = x^2[/tex], then [tex]f(4) = 4^2 = 16[/tex].

Find:
a. [tex]f(1)[/tex]
b. [tex]f(-3)[/tex]
c. [tex]f(t)[/tex]

Answer :

Sure, let's solve the question step by step.

We are given the function [tex]\( f(x) = x^2 \)[/tex]. We need to find the values of this function for different inputs.

### a. Find [tex]\( f(1) \)[/tex]

1. Plug [tex]\( x = 1 \)[/tex] into the function:
[tex]\[
f(1) = 1^2
\][/tex]

2. Calculate the square of 1:
[tex]\[
1^2 = 1
\][/tex]

So,
[tex]\[
f(1) = 1
\][/tex]

### b. Find [tex]\( f(-3) \)[/tex]

1. Plug [tex]\( x = -3 \)[/tex] into the function:
[tex]\[
f(-3) = (-3)^2
\][/tex]

2. Calculate the square of [tex]\(-3\)[/tex]:
[tex]\[
(-3)^2 = 9
\][/tex]

So,
[tex]\[
f(-3) = 9
\][/tex]

### c. Find [tex]\( f(t) \)[/tex]

1. Plug [tex]\( x = t \)[/tex] into the function:
[tex]\[
f(t) = t^2
\][/tex]

Since [tex]\( t \)[/tex] is a variable, we just leave the expression in terms of [tex]\( t \)[/tex]:

So,
[tex]\[
f(t) = t^2
\][/tex]

### Summary of Results

- [tex]\( f(1) = 1 \)[/tex]
- [tex]\( f(-3) = 9 \)[/tex]
- [tex]\( f(t) = t^2 \)[/tex]

These are the values of the function for the given inputs.

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Rewritten by : Barada