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Question Number 169319 by otchereabdullai@gmail.com last updated on 28/Apr/22

$$\mathrm{if}\mathrm{f}(2\mathrm{x}-1)={\mathrm{x}}^2-3\mathrm{x}+2,\mathrm{find}\mathrm{f}\left(2\right)$$

Commented by infinityaction last updated on 28/Apr/22

$$x\to \frac{x+1}{2}$$$$f\left(x\right)={\left(\frac{x+1}{2}\right)}^2-3\left(\frac{x+1}{2}\right)+2$$$$f\left(2\right)=\frac{9}{4}-\frac{9}{2}+2$$$$f\left(2\right)=-\frac{1}{4}$$

Commented by otchereabdullai@gmail.com last updated on 28/Apr/22

$$\mathrm{Thank}\mathrm{you}$$

Answered by alephzero last updated on 28/Apr/22

$$f(2x-1)=x^2-3x+2$$$$2=2x-1$$$$\Rightarrow x=1.5$$$$\Rightarrow f(2(1.5)-1)=1.5^2-3(1.5)+2$$$$=2.25-4.5+2=-0.25$$

Commented by otchereabdullai@gmail.com last updated on 28/Apr/22

$$\mathrm{thank}\mathrm{you}$$

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