To determine the input value for the function [tex]\( g(x) = 0.4x - 1.8 \)[/tex] that yields an output of 4.67, follow these steps:
1. Set the function equal to the desired output:
[tex]\[
0.4x - 1.8 = 4.67
\][/tex]
2. Isolate the term involving [tex]\( x \)[/tex]:
Add 1.8 to both sides of the equation to eliminate the constant term on the left side:
[tex]\[
0.4x = 4.67 + 1.8
\][/tex]
3. Simplify the right-hand side:
[tex]\[
4.67 + 1.8 = 6.47
\][/tex]
Thus, the equation now is:
[tex]\[
0.4x = 6.47
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
Divide both sides of the equation by 0.4 to isolate [tex]\( x \)[/tex]:
[tex]\[
x = \frac{6.47}{0.4}
\][/tex]
5. Calculate the quotient:
[tex]\[
x = 16.175
\][/tex]
Therefore, the input needed for the function [tex]\( g(x) = 0.4x - 1.8 \)[/tex] to produce an output of 4.67 is approximately [tex]\( x = 16.175 \)[/tex].
