f:R->R f(x)=7x-3 Prove that f is onto.

$$\displaystyle{f}:{R}\to{R}$$
f(x)=7x-3
Prove that f is onto.

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dessinemoie
$$\displaystyle{f}:{R}\to{R}$$
f(x)=7x-3
Let $$\displaystyle{y}\in{R}$$ and
$$\displaystyle{x}=\frac{{{y}+{3}}}{{7}}$$
$$\displaystyle{x}=\frac{{{y}+{3}}}{{7}}\in{R}$$
f(x)=7x-3
$$\displaystyle={7}{\left(\frac{{{y}+{3}}}{{7}}\right)}-{3}$$
=y+3-3
=y
Since f(x)=y, and $$\displaystyle{y}\in{R}$$, f is onto