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

Rivka Thorpe 2021-09-21 Answered
\(\displaystyle{f}:{R}\to{R}\)
f(x)=7x-3
Prove that f is onto.

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Expert Answer

dessinemoie
Answered 2021-09-22 Author has 12571 answers
\(\displaystyle{f}:{R}\to{R}\)
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
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