If `f (x) = ax + 6 and f (1) =11,` then `a = `

Options

A. 6
B. 17
C. 11
D. 5

Answer

To solve the problem step by step, we start with the function given and the condition provided.

**Step 1: Write down the function and the condition.**
We have the function:
\[ f(x) = ax + 6 \]
And we know that:
\[ f(1) = 11 \]

**Step 2: Substitute \( x = 1 \) into the function.**
To find \( f(1) \), we substitute \( x = 1 \) into the function:
\[ f(1) = a(1) + 6 \]
This simplifies to:
\[ f(1) = a + 6 \]

**Step 3: Set the expression equal to 11.**
According to the problem, we know that:
\[ f(1) = 11 \]
So we can set up the equation:
\[ a + 6 = 11 \]

**Step 4: Solve for \( a \).**
Now, we need to isolate \( a \) in the equation:
\[ a + 6 = 11 \]
Subtract 6 from both sides:
\[ a = 11 - 6 \]
Thus, we find:
\[ a = 5 \]

**Final Answer:**
The value of \( a \) is \( 5 \).

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