The function $$ f $$ is given by $$ f(x)=x+2 \cdot $$ if $$ f-1(n)=4 $$, what is the value of $$ n $$ ?

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UpStudy AI · Accepted Answer

To solve for $$ n $$ given the function $$ f(x) = x + 2 $$ and the condition $$ f^{-1}(n) = 4 $$, we will follow these steps:

1. **Find the inverse function $$ f^{-1}(x) $$**:
   - The function $$ f(x) = x + 2 $$ can be rearranged to find its inverse. We set $$ y = f(x) $$:
     $$
     y = x + 2
     $$
   - To find $$ x $$ in terms of $$ y $$, we rearrange the equation:
     $$
     x = y - 2
     $$
   - Thus, the inverse function is:
     $$
     f^{-1}(x) = x - 2
     $$

2. **Use the condition $$ f^{-1}(n) = 4 $$**:
   - Substitute $$ n $$ into the inverse function:
     $$
     f^{-1}(n) = n - 2
     $$
   - Set this equal to 4:
     $$
     n - 2 = 4
     $$

3. **Solve for $$ n $$**:
   - Add 2 to both sides:
     $$
     n = 4 + 2
     $$
   - Therefore:
     $$
     n = 6
     $$

The value of $$ n $$ is $$ 6 $$.
$$ n = 6 $$

The function \( f \) is given by \( f(x)=x+2 \cdot \) if \( f-1(n)=4 \), what is the value of \( n \) ?

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