Answer
$1$ learning trial
The point the graph: $(1,0.5)$.
Work Step by Step
Replace $f(x)$ with $0.5$ in the function's formula.
$\Rightarrow 0.5=\frac{0.9x-0.4}{0.9x+0.1}$
Multiply both sides by $(0.9x+0.1)$ to clear denominators.
$\Rightarrow (0.9x+0.1)0.5=(0.9x+0.1)\cdot \frac{0.9x-0.4}{0.9x+0.1}$
Simplify.
$\Rightarrow 0.45x+0.05=0.9x-0.4$
Add $-0.45x+0.4$ to both sides.
$\Rightarrow 0.45x+0.05-0.45x+0.4=0.9x-0.4-0.45x+0.4$
Simplify.
$\Rightarrow 0.45=0.45x$
Divide both sides by $0.45$.
$\Rightarrow \frac{0.45}{0.45}=\frac{0.45x}{0.45}$
Simplify.
$\Rightarrow 1=x$
Hence, the learning trials are $1$.
The point the graph is $(1,f(1))=(1,0.5)$.
