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If h(z)=(4z-2)/(z-A) and h(3)=-2 what is the value of A? A=square (Simplify your answer.)

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If h(z)=(4z-2)/(z-A) and h(3)=-2 what is the value of A?
A=square  (Simplify your answer.)

If h(z)=(4z-2)/(z-A) and h(3)=-2 what is the value of A? A=square (Simplify your answer.)

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RafaelElite · Tutor por 8 anos

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To find the value of \( A \), we need to substitute \( z = 3 \) into the function \( h(z) \) and set it equal to -2.<br /><br />Given:<br />\[ h(z) = \frac{4z - 2}{z - A} \]<br />and<br />\[ h(3) = -2 \]<br /><br />Substitute \( z = 3 \) into the function:<br />\[ h(3) = \frac{4(3) - 2}{3 - A} = -2 \]<br /><br />Simplify the numerator:<br />\[ \frac{12 - 2}{3 - A} = -2 \]<br />\[ \frac{10}{3 - A} = -2 \]<br /><br />Now, solve for \( A \):<br />\[ 10 = -2(3 - A) \]<br />\[ 10 = -6 + 2A \]<br />\[ 10 + 6 = 2A \]<br />\[ 16 = 2A \]<br />\[ A = 8 \]<br /><br />Therefore, the value of \( A \) is:<br />\[ A = 8 \]
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