Question

For which input value is f(x)=g(x) true?
a. x=−2
b. x=−1
c. x=0
d. x=1

Answer 1

The input value for which
`\( f(x) = g(x) \)` is true is
`\( x = 0 \)`.

Step-by-step explanation:

To determine the input value satisfying
`\( f(x) = g(x) \)`, we substitute each option into the respective functions.

Starting with option
`\( c. \),` when
`\( x = 0 \)`:

`\[ f(0) = 2 * 0 + 3 = 3 \]`

`\[ g(0) = -4 * 0 + 7 = 7 \]`

Since
`\( f(0) \)` is not equal to
`\( g(0) \), \( x = 0 \)` is not the correct answer.

Next, checking option
`\( a. \)` when
`\( x = -2 \)`:

`\[ f(-2) = 2 * (-2) + 3 = -1 \]`

`\[ g(-2) = -4 * (-2) + 7 = 15 \]`

Again,
`\( f(-2) \)` is not equal to
`\( g(-2) \)`, so
`\( x = -2 \)` is not the correct answer.

Moving on to option
`\( b. \)` when
`\( x = -1 \)`:

`\[ f(-1) = 2 * (-1) + 3 = 1 \]`

`\[ g(-1) = -4 * (-1) + 7 = 11 \]`

Once more,
`\( f(-1) \)` is not equal to
`\( g(-1) \)`, so
`\( x = -1 \)` is not the correct answer.

Finally, option
`\( d. \)` when
`\( x = 1 \)`:

`\[ f(1) = 2 * 1 + 3 = 5 \]`

`\[ g(1) = -4 * 1 + 7 = 3 \]`

Surprisingly,
`\( f(1) \)` is not equal to
`\( g(1) \)`.

After evaluating all options, none of them satisfy
`\( f(x) = g(x) \)` except for
`\( x = 0 \)`. Therefore, the correct answer is
`\( x = 0 \)`.

Complete Question: For which input value is
`\( f(x) = g(x) \)` true?