Each range value given was substituted into the function for f(x) and the equation formed was solved for x.
The values of the domain of the given function are:
A. 1
E. 5
F. 6
G. 7
Given:
[tex]f(x) = -7x + 9[/tex]
Range: {[tex]2, -26,-33,-40[/tex]}
To find the domain values of the function, you would do the following:
- Substitute each given range value of the function for [tex]f(x)[/tex]
- Solve each equation to determine the value of x in each case
- The values of x you get from each resulting equation will constitute the domain values of the given function.
Thus:
- For range value [tex]f(x)[/tex], of 2, find x by substituting [tex]f(x) = 2[/tex] into [tex]f(x) = -7x + 9[/tex]
[tex]2 = -7x + 9[/tex]
Subtract 9 from each side
[tex]2 - 9 = -7x + 9 - 9\\-7 = -7x[/tex]
Divide both sides by -7
[tex]\frac{-7}{-7} = \frac{-7x}{-7} \\1 = x\\x = 1[/tex]
- For range value [tex]f(x)[/tex], of -26, find x by substituting [tex]f(x) = -26[/tex] into [tex]f(x) = -7x + 9[/tex]
[tex]-26 = -7x + 9[/tex]
Subtract 9 from each side
[tex]-26 - 9 = -7x + 9 - 9\\-35 = -7x[/tex]
Divide both sides by -7
[tex]\frac{-35}{-7} = \frac{-7x}{-7} \\5 = x\\x = 5[/tex]
- For range value [tex]f(x)[/tex], of -33, find x by substituting [tex]f(x) = -33[/tex] into [tex]f(x) = -7x + 9[/tex]
[tex]-33 = -7x + 9[/tex]
Subtract 9 from each side
[tex]-33 - 9 = -7x + 9 - 9\\-42 = -7x[/tex]
Divide both sides by -7
[tex]\frac{-42}{-7} = \frac{-7x}{-7} \\6 = x\\x = 6[/tex]
- For range value [tex]f(x)[/tex], of -40, find x by substituting [tex]f(x) = -40[/tex] into [tex]f(x) = -7x + 9[/tex]
[tex]-40 = -7x + 9[/tex]
Subtract 9 from each side
[tex]-40 - 9 = -7x + 9 - 9\\-49 = -7x[/tex]
Divide both sides by -7
[tex]\frac{-49}{-7} = \frac{-7x}{-7} \\7 = x\\x = 7[/tex]
Therefore, the values of the domain of the given function are:
A. 1
E. 5
F. 6
G. 7
Learn more about functions here:
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