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Use the functions below.

f(x)=5x+7

g(x)=5x−2

h(x)=5x+3

What is (f−g+h)(x)
?

Enter the missing values.

(1 point)
$$

1 answer

To find \((f-g+h)(x)\), we will first calculate \(f(x) - g(x) + h(x)\).

  1. Calculate \(f(x) - g(x)\): \[ f(x) = 5x + 7 \] \[ g(x) = 5x - 2 \] \[ f(x) - g(x) = (5x + 7) - (5x - 2) = 5x + 7 - 5x + 2 = 9 \]

  2. Now, add \(h(x)\): \[ h(x) = 5x + 3 \] \[ (f-g)(x) + h(x) = 9 + (5x + 3) = 9 + 5x + 3 = 5x + 12 \]

Putting it all together, we find: \[ (f - g + h)(x) = 5x + 12 \]

Thus, the final answer is: \[ \boxed{5x + 12} \]