Questions: For the equation shown below, solve for y as a function of x and express the result using function notation 32 * x + 4 * y = 16 f(x)= Given f(x)=2 x-2 a) Evaluate f(4)

For the equation shown below, solve for y as a function of x and express the result using function notation 32 * x + 4 * y = 16
f(x)=

Given f(x)=2 x-2
a) Evaluate f(4)

Transcript text: For the equation shown below, solve for $y$ as a function of $x$ and express the result using function notation $32 \cdot x+4 \cdot y=16$ $f(x)=$ $\square$ Given $f(x)=2 x-2$ a) Evaluate $f(4)$

Solution

Solution Steps

Question 10

For the equation $32 \cdot x + 4 \cdot y = 16$, solve for $y$ as a function of $x$ and express the result using function notation $f(x)$.

Solution Approach

Isolate $y$ on one side of the equation.
Express $y$ in terms of $x$.
Write the resulting expression in function notation $f(x)$.

Step 1: Solve for $ y $ in terms of $ x $

Given the equation: \[ 32 \cdot x + 4 \cdot y = 16 \]

First, isolate $ y $ on one side of the equation. Subtract $ 32x $ from both sides: \[ 4y = 16 - 32x \]

Next, divide both sides by 4 to solve for $ y $: \[ y = \frac{16 - 32x}{4} \]

Simplify the fraction: \[ y = 4 - 8x \]

Step 2: Express $ y $ as a function of $ x $

Using function notation, we write: \[ f(x) = 4 - 8x \]

Final Answer

\[ \boxed{f(x) = 4 - 8x} \]

Step 1: Evaluate $ f(4) $

Given the function: \[ f(x) = 2x - 2 \]

Substitute $ x = 4 $ into the function: \[ f(4) = 2(4) - 2 \]

Step 2: Simplify the expression

Calculate the value: \[ f(4) = 8 - 2 \] \[ f(4) = 6 \]

Final Answer

\[ \boxed{f(4) = 6} \]

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >

Thank you for your feedback.

Copied!