12 f(x)=(2x+1)(x+1) find: a f(2) b f(-2) f(0)

To find the values of \( f(x) \) for the given function \( f(x) = (2x+1)(x+1) \), we need to substitute the given values of \( x \) into the function and simplify.<br /><br />a) \( f(2) \):<br />Substitute \( x = 2 \) into the function:<br />\[ f(2) = (2(2)+1)(2+1) \]<br />\[ f(2) = (4+1)(3) \]<br />\[ f(2) = 5 \cdot 3 \]<br />\[ f(2) = 15 \]<br /><br />b) \( f(-2) \):<br />Substitute \( x = -2 \) into the function:<br />\[ f(-2) = (2(-2)+1)((-2)+1) \]<br />\[ f(-2) = (-4+1)(-1) \]<br />\[ f(-2) = -3 \cdot (-1) \]<br />\[ f(-2) = 3 \]<br /><br />c) \( f(0) \):<br />Substitute \( x = 0 \) into the function:<br />\[ f(0) = (2(0)+1)(0+1) \]<br />\[ f(0) = (0+1)(1) \]<br />\[ f(0) = 1 \cdot 1 \]<br />\[ f(0) = 1 \]<br /><br />Therefore, the answers are:<br />a) \( f(2) = 15 \)<br />b) \( f(-2) = 3 \)<br />c) \( f(0) = 1 \)