Questions: f(x)=5 sqrt(8-7 x)+10

Transcript text: f(x)=5 \sqrt{8-7 x}+10

Solution

Solution Steps

To solve for \( f(x) \), we need to evaluate the function for a given value of \( x \). The function involves a square root and a linear transformation. We will substitute the value of \( x \) into the function and compute the result.

Step 1: Define the Function

The function given is \( f(x) = 5 \sqrt{8 - 7x} + 10 \). We need to evaluate this function for a specific value of \( x \).

Step 2: Substitute the Value of \( x \)

Substitute \( x = 1 \) into the function: \[ f(1) = 5 \sqrt{8 - 7 \times 1} + 10 \]

Step 3: Simplify the Expression

Calculate the expression inside the square root: \[ 8 - 7 \times 1 = 1 \] Thus, the function becomes: \[ f(1) = 5 \sqrt{1} + 10 \]

Step 4: Evaluate the Square Root

Since \(\sqrt{1} = 1\), the expression simplifies to: \[ f(1) = 5 \times 1 + 10 \]

Step 5: Calculate the Final Result

Perform the multiplication and addition: \[ f(1) = 5 + 10 = 15 \]

Final Answer

The value of the function at \( x = 1 \) is \(\boxed{15}\).

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