Question

f (x) =x 2 squared - 2x +3 find f (3 dived by 4 )

Answer 1

To evaluate the function \( f(x) = x^2 - 2x + 3 \) at \( x = \frac{3}{4} \), we will substitute \( \frac{3}{4} \) into the function.

1. Substitute \( x = \frac{3}{4} \):

\[
f\left(\frac{3}{4}\right) = \left(\frac{3}{4}\right)^2 - 2\left(\frac{3}{4}\right) + 3
\]

2. Calculate \( \left(\frac{3}{4}\right)^2 \):

\[
\left(\frac{3}{4}\right)^2 = \frac{9}{16}
\]

3. Calculate \( -2\left(\frac{3}{4}\right) \):

\[
-2\left(\frac{3}{4}\right) = -\frac{6}{4} = -\frac{3}{2}
\]

4. Rewrite \(-\frac{3}{2}\) with a common denominator of 16:

\[
-\frac{3}{2} = -\frac{3 \times 8}{2 \times 8} = -\frac{24}{16}
\]

5. Now, substitute back and simplify:

\[
f\left(\frac{3}{4}\right) = \frac{9}{16} - \frac{24}{16} + 3
\]

6. Convert 3 to a fraction with a denominator of 16:

\[
3 = \frac{3 \times 16}{16} = \frac{48}{16}
\]

7. Now combine the fractions:

\[
f\left(\frac{3}{4}\right) = \frac{9}{16} - \frac{24}{16} + \frac{48}{16} = \frac{9 - 24 + 48}{16} = \frac{33}{16}
\]

So,

\[
f\left(\frac{3}{4}\right) = \frac{33}{16}
\]