(b) Diberi/ Given: $$ f: x ightarrow \frac{2 x}{x+3}, x
eq-3 $$ $$ g: x ightarrow 5 x-1 $$ Cari nilai $$ x $$ apabila $$ g f(x)=3 $$ Find the value of $$ x $$ when $$ g f(x)=3 $$

Question

(b) Diberi/ Given: $$ f: x ightarrow \frac{2 x}{x+3}, x 
eq-3 $$ $$ g: x ightarrow 5 x-1 $$ Cari nilai $$ x $$ apabila $$ g f(x)=3 $$ Find the value of $$ x $$ when $$ g f(x)=3 $$

UpStudy AI · Accepted Answer

Step 1: Define the functions

We have
$$
f(x)=\frac{2x}{x+3}, \quad x\neq -3,
$$
and
$$
g(x)=5x-1.
$$

Step 2: Write the expression for $$ g(f(x)) $$

Substitute $$ f(x) $$ into $$ g $$:
$$
g(f(x))=5\left(\frac{2x}{x+3}\right)-1.
$$

Step 3: Set up the equation $$ g(f(x))=3 $$

$$
5\left(\frac{2x}{x+3}\right)-1=3.
$$

Step 4: Solve the equation

First, add $$ 1 $$ to both sides:
$$
5\left(\frac{2x}{x+3}\right)=4.
$$

Multiply both sides by $$ x+3 $$ (note $$ x\neq -3 $$):
$$
5(2x)=4(x+3).
$$

Simplify:
$$
10x=4x+12.
$$

Subtract $$ 4x $$ from both sides:
$$
6x=12.
$$

Divide both sides by $$ 6 $$:
$$
x=2.
$$

Step 5: Verify There Are No Domain Issues

Since $$ x=2 $$ and the domain restriction is $$ x\neq -3 $$, the solution is valid.

Thus, the answer is 
$$
x=2.
$$
$$ x=2 $$

(b) Diberi/ Given:

Cari nilai apabila
Find the value of when

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(b) Diberi/ Given: Cari nilai apabila Find the value of when